(a) Sound with intensity larger than `120 dB` appears painful to a person. A small speaker delivers `2.0 W` of audio output. How close can the person get to the speaker without hurting his ears? (b) If the sound level in a room is increased from `50 dB` to `60 dB`, by what factor level is the pressure amplitude increased?

(a) Sound with intensity larger than `120 dB` appears painful to a per

1.	(a) Sound with intensity larger than `120 dB` appears painful to a person. A small speaker delivers `2.0 W` of audio output. How close can the person get to the speaker without hurting his ears? (b) If the sound level in a room is increased from `50 dB` to `60 dB`, by what factor level is the pressure amplitude increased?
Answer» (a) `L = 10 log_(10)((I)/(I_ (0)))` `120 = 10 log_(10)((I)/(10^(-12)))` `(I)/(10^(12)) = 10^(12) rArr I = 1 W//m^(2)` For a point source of power `P`, intensity at distance `r` `I = (P)/(4pi r^(2))` `r = sqrt ((P)/(4pi I)) = sqrt ((2)/(4pi xx 1)) = sqrt ((1)/(2pi)) = 0.4 m` (b) `L_(2) - L_(1) = 10 log_(10)(I_(2)/(I_(1)))` `60 - 50 = 10 log_(10)(I_(2)/(I_(1))) rArr log_(10)(I_(2)/(I_(1))) = 1` `I_(2)/(I_(1)) = 10` `I prop p_(0)^(2)` `I_(2)/(I_(1)) = [(p_(0))_(2)^(2)/(p_(0))_(1)^(2)] = 10` `(p_(0))_(2)/(p_(0))_(1) = sqrt (10)`

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